netplot: Beautiful graph drawing

  • An alternative graph visualization engine that puts an emphasis on aesthetics at the same time of providing default parameters that provide visualizations that are out-of-the-box nice.

Some features:

  • Auto-scaling of vertices using sizes relative to the plotting device.
  • Embedded edge color mixer.
  • True curved edges drawing.
  • User-defined edge curvature.
  • Nicer vertex frame color.
  • Better use of space filling the plotting device.

The package uses the grid plotting system (just like ggplot2).

Comparison

UK Faculty

Some features

Node scaling

Some features

Node shapes

Some features

Edge curvature

Some features

Edge type of line

US airports

Applied Social Network Analysis with R

Little ERGMs

The distribution of \(\mathbf{Y}\) can be parameterized in the form

\[ \Pr\left(\mathbf{Y}=\mathbf{y}|\theta, \mathcal{Y}\right) = \frac{\exp{\theta^{\mbox{T}}\mathbf{g}(\mathbf{y})}}{\kappa\left(\theta, \mathcal{Y}\right)},\quad\mathbf{y}\in\mathcal{Y} \tag{1} \]

Where \(\theta\in\Omega\subset\mathbb{R}^q\) is the vector of model coefficients and \(\mathbf{g}(\mathbf{y})\) is a q-vector of statistics based on the adjacency matrix \(\mathbf{y}\).

  • Model (1) may be expanded by replacing \(\mathbf{g}(\mathbf{y})\) with \(\mathbf{g}(\mathbf{y}, \mathbf{X})\) to allow for additional covariate information \(\mathbf{X}\) about the network. The denominator,

    \[ \kappa\left(\theta,\mathcal{Y}\right) = \sum_{\mathbf{z}\in\mathcal{Y}}\exp{\theta^{\mbox{T}}\mathbf{g}(\mathbf{z})} \]

  • Is the normalizing factor that ensures that equation (1) is a legitimate probability distribution.

  • Even after fixing \(\mathcal{Y}\) to be all the networks that have size \(n\), the size of \(\mathcal{Y}\) makes this type of models hard to estimate as there are \(N = 2^{n(n-1)}\) possible networks!

The lergm R package

  • An Extension of the ergm (regular size fitting via simulation) package

  • Uses exact statistics for fitting small networks (3 to 6 nodes).

  • Will be designed mostly to be ran with multiple networks simulatenously (so we recover the asymptotic properties of the MLE estimators)

  • Work in progress…

Thanks!

Twitter: @gvegayon

email: vegayon@usc.edu